The commonly useful methods for the model reduction of large-scale linear time invariant dynamical systems are the balanced truncation and \(\mathcal {H}_2\)  optimal model reduction [1]}. Both the methods are well established and successfully investigated to find the model reduction of large-scale sparse dynamical systems. In the recent times frequency and time limited model reduction methods have taken a lot of attentions due to its demand in real-life applications. In many applications, a specific frequency interval is more important, i.e., the ROM should maintain a superior accuracy within that desired frequency interval. Balanced truncation based frequency limited model reduction was discussed by Gawronski and Juang in [2]}. The computational techniques for the time and frequency limited balanced truncation were discussed in [3]}.
